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This problem trains for: SAT-I, AMC-8, GMAT.

The positive difference of the roots of the equation

equation

is:

Notice the difference of squares identity on the right hand side:

equation

Also:

equation

Therefore, the equation can be written:

equation

and we can divide both sides by 7x-2 if we keep in mind that we thus lose the root:

equation

The remaining equation is:

equation

equation

equation

with another root of:

equation

and positive difference of the roots:

equation